It took the economics profession a hundred years to understand value as marginal utility, and a while longer to understand it wasn’t measurable. Philosophers and scientists had been thinking about the physical world for millennia, but it wasn’t until Newton that the greatest strides were made to some first principles — only to have his perspective on matter and force transformed by Einstein a few centuries later.

And I know that many ideas go in and out of my head, too. I bet even geniuses have to struggle to learn well past graduation day.

Often, we have to relearn.

So let’s give each other a few breaks. When someone does not immediately understand something you are fairly certain is true, rephrase. Re-explain. And take some time, with patience, to rethink and reformulate the principle, until it makes sense to more than just yourself. And members of your own tribe.

On Tuesday’s The Five, a Fox news opinion chat show, the subject was guns, the occasion for discussion being safety in the wake of the much-talked-about Mall of America terrorist threat. Former RedEye host (his last show was early Saturday morning) and The Five creator Greg Gutfeld decried, to his four other arguing co-hosts, the very idea of “gun-free zones.” The problem with designating an area “free of guns” means only that peaceful people will abide by the designation. This leaves bad guys with a target. Gutfeld advanced the “more guns, less crime” argument that economist John Lott has more famously made. Gun-free zones are stupid; we’d all be better off if more of us carried guns around, especially if we carried them discreetly, concealed.

Juan Williams, a Fox political analyst sitting in liberal Bob Beckel’s usual seat, expressed a typical bit of liberalish incredulity. “I don’t think that makes sense, that everybody in the mall has a gun. Let the police protect us.”

Gutfeld laughed. There was banter. Some accusatory explanation. Oh, you lefties! But then Gutfeld regrouped.

“This is not an either/or — like everybody’s armed [or] everybody’s not. The concealed [carry] permit creates a level of uncertainty on the people that are choosing an attack.”

I agree with Gutfeld. But I suspect that the skeptical need more than a few sound-bites and short arguments to convince them.

Other things being equal, the secretly (or discreetly) gun totin’ are safer than the rest of society. The more folks who secretly carry means that those prone to violence face higher risks.

There may be more than one reason why gun violence has plummeted over the past two decades. But one must be this: as Americans have accumulated more guns per capita than ever before, as more households possess guns than ever, the “celerity of punishment” has increased, nudging the marginally criminal to choose to commit fewer violent crimes.

Making society safer.

Since Mr. Williams — who is, after all, a very bright man — seemed to have some difficulty with this, let’s go over the logic of it all.

First, I used an old term, above, from Jeremy Bentham. “Celerity of punishment” signifies swiftness of bad repercussions. What the old philosopher and reformer argued in the late 18th century was that severity of punishment is not nearly as effective in deterring crime as certainty and speediness in punishment.

And “punishment” isn’t merely what the judge says — it can be a crippling or deadly bullet shot by a citizen in self-defense at the time of the criminal act.

Second, let’s acknowledge that the police rarely defend us. Most police work is clean-up. They find the bad guys (when they do) only after the crime.

And why is that? Greg Gutfeld did a great job making this clear. Criminals not only flock to gun-free zones — Gutfeld even cited evidence that home-grown American terrorists and spree shooters have calculated like this: they may seem “crazy” but even in their craziness they wish to kill as many people as possible before they are killed themselves — they avoid obvious threats. So when they see armed police, they wait to do their crimes until the police have moved on.

It is the principle of self-preservation.

Even murder-suicides tend to try to postpone that last shot.

Third, would-be criminals and terrorists try to avoid people with guns, but when the guns are hidden, the guns are hard to avoid. Because hard to detect. Then they face an element of risk. The more concealed-carry permits in a community, the greater the likelihood of a public shooter being quickly shot himself. The mere existence of an unknown — but statistically significant — number of guns hidden on the persons and in the clothing of potential victims, gives intruders, robbers, murderers, would-be spree murderers and maybe even terrorists more than a little pause.

Fourth, one of the chief uses of guns by peaceful people is . . . the mere ownership and brandishing. Most defensive uses of guns cannot show up in statistics, since most times a shot is never fired. Most violent people do not want to be killed. So when somebody takes out a gun and points it at them, they often will run away, or even lay down their arms.

Relying on the police is not very effective. Relying on ourselves and our peaceful fellow citizens can be much more effective.

But perhaps an analogy will help Juan Williams understand the principle: compare gun violence and peaceful gun ownership to viral infection and vaccination.

It’s herd immunity, only to violence. Just as the more people vaccinated make us all safer, the more peaceful people discreetly carrying guns make us all safer.

The “herd immunity” principle applies when the number of people immune to a disease in a population reaches a high enough level that it prevents epidemic spread of a disease, for most potential targets fight off the blight, and most nodes of infection become dead ends.

As disbelief in the efficacy (or fear of side effects) of vaccines for measles, mumps, whooping cough, etc., has grown, American and first-world societies have lost some herd immunity. Epidemics in measles and other once-conquered diseases are now popping up, here and there.

But as the number of households with guns has reached its highest levels in American history, crime rates have gone down. Has our “herd” become somewhat more immune to violence?

It’s a principle that surely must be in play. There is evidence to support it. Concealed carry, more even than open carry and the general right to bear arms (courtesy of our Second Amendment) — and even more than increased levels of policing or incarceration — drives the downward trend in violence.

For, the old utilitarian Jeremy Bentham was almost surely right. It’s not severity of punishment that is most effective at preventing crime. It is “celerity.” But Bentham was probably wrong to expect this from government. The best deliverer of swift punishment is not the constabulary. It is, instead, those armed-but-peaceful citizens concerned about protecting themselves and those around them. And certainty in punishment is not an option. But more likely bad — even maximally severe — repercussions are something we ourselves can provide.